Definitely doable
Inside the unit there is most likely a contactor or relay that is energized by the timer on the unit, which causes the contacts on the contactor to close, allowing power through to the unit compressor and fan, the unit thus turns on. when the signal from the timer turns off, contacts open, no power can get through, unit turns off.
What you'll ultimately need to do is remove the wiring that goes from the timer to the contactor's coil, and replace it with wire coming from your new thermostat, so that it operates the contactor instead of the timer.
The first thing you'll need to do is find out what the coil rating is on the contactor. Open up the unit and on the back of the timer will be wires. They will most likely go to a small box like 2x2 inches square or thereabouts, the box will have wires going to the compressor and fan(s). This box is the contactor or relay. It is the "bridge" between your timer or thermostat and power going to the unit. It connects the two. There should be two separate ratings on it. One will usually be a chart with voltage and FLA (Full Load Amperage), this is not what you are after. This rating is for the power poles, not the coil. You want the coil voltage.
There should be a rating that mentions only voltage, and it should specifically say "coil voltage" or perhaps just "coil".
If the coil rating is 120v it would be easy to then buy something like an STC-1000 controller off youtube, and for $50-$75 and an hour or 2 of work you'd have a digital controller with pretty flexible programming options, even has adjustable compressor restart protection so your a/c isn;t going on/of on/off every 3 minutes, which is hard on compressors. If it's a low voltage coil, 24v or 12v it is still doable, just a tad more complicated, will need to talk more options in that case.
Let me know if you can find that, I'd be glad to help you get this set up.